Hyers–Ulam Stability of Isometries on Bounded Domains–III

Ginkyu Choi and Soon-Mo Jung ()
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Ginkyu Choi: Department of Electronic and Electrical Engineering, College of Science and Technology, Hongik University, Sejong 30016, Republic of Korea
Soon-Mo Jung: Nano Convergence Technology Research Institute, School of Semiconductor·Display Technology, Hallym University, Chuncheon 24252, Republic of Korea

Mathematics, 2024, vol. 12, issue 12, 1-10

Abstract: The question of whether there is a true isometry that approximates the ε -isometry defined on a bounded set has long interested mathematicians. The first paper on this topic was published by Fickett, whose result was subsequently greatly improved by Alestalo et al., Väisälä and Vestfrid. Recently, the authors published some papers improving the previous results. The main purpose of this paper is to improve all of the abovementioned results by utilizing the properties of the norm and inner product for Euclidean space.

Keywords: Hyers–Ulam stability; isometry; ? -isometry; Euclidean space; bounded domain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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